Fun symmetry activities help students to recognize the properties of congruent shapes. Begin by having students discuss lines of symmetry in basic geometric shapes, such as triangles and squares, before progressing to more complex shapes. Give them an activity sheet or draw a selection of shapes onto the board and have them draw as many lines of symmetry as they can on each shape. Ask them to choose a symmetrical shape and get them to cut it out using construction paper. Have them cut along one of the lines of symmetry and try to fit the two halves on top of each other; if they fit perfectly together, explain to students that they are congruent shapes. As students advance in their understanding of congruency, consider having them complete a symmetrical design involving congruent shapes in a paper quilt project, or design a flag made up of congruent shapes.
Exploring the three transformations through interactive games helps children in their understanding of congruent shapes. Teach students that there are three transformations that can create congruent shapes: rotation, reflection and translation. Have children rotate simple geometric shapes around a center point using a graph to demonstrate rotation. Approach reflection by having students practice reflecting shapes on a graph using the mirror line. They can use a mirror, fold the paper along the mirror line or label the corners of the shape and use them to accurately reflect the shape over the mirror line on an axis. For translation, have children move a shape around on a graph, making sure that each point of the shape moves the same distance and in the same direction. When students have grasped the concept of transformation, have them cut out four congruent polygons and glue them onto a sheet of paper so that the shapes demonstrate examples of turning, flipping and sliding. A game of Tetris is a fun way to visually show each transformation.
Games involving replication are a useful and interactive way for children to identify congruent shapes. Choose a child to draw a shape of their choice onto a piece of lineless paper. Have all the other students try to accurately replicate the shape onto construction paper so that they are identical. Check that the shapes are congruent by getting students to cut out their shapes and place them over the top of the first shape. The child who manages to create the congruent shape accurately can glue the shape over the top of the original.
Students must learn the difference between similar and congruent shapes in order to progress in math. Collect an assortment of objects, some of which that are congruent and some that are similar. Hold two objects up, such as two balls of different sizes, and ask students whether they are similar or congruent and why. When they can comprehend the difference, have them build congruent and similar shapes with blocks, getting them to gradually build the complexity of their shapes.